Problem 4 - Precalculus Essentials

Question

Find the domain of each function. $$g(x)=\frac{2}{x+5}$$

Step-by-Step Solution

Answer

The domain of the function \(g(x) = \frac{2}{x + 5}\) is all real numbers except \(x = -5\).

Step 1: Identify the Denominator

Determine the denominator of the function \(g(x)\). The denominator is \(x + 5\).

Step 2: Set the Denominator Equal to Zero

To find the value where the denominator is zero, solve the equation \(x + 5 = 0\). As a result, \(x = -5\).

Step 3: Exclude Value from the Domain

The domain of \(g(x)\) is all real numbers except \(x = -5\). So, the domain is \(x \in R - {-5}\).